During a collision a strong collision force acts between the objects involved
in the collision. The collision force is related to the change in the linear
momentum of the objects on which it is acting. Newton concluded that when two
objects exert a force on each other, than the force experienced by each object
is equal in magnitude but directed in an opposite direction. This implies that
when two objects collide, the change in the linear momentum of each object is
equal in magnitude, but opposite in sign. Thus, the total linear momentum of
the system is unchanged:

total linear momentum before the collision = total linear momentum
after the collision

We have tested this relation today by looking at elastic collisions. In elastic
collisions, the total kinetic energy (0.5*m*v^2) is conserved, and this allows
one to make predictions about the outcome of the experiment given the initial
conditions. Using the data we collected on 3/24/2003 carry out the following
calculations (use Excel to make it easier to complete these calculations):

Calculate the linear momentum of each cart before and after the collision
(you might already have done this on Monday).

Calculate the total linear momentum of the system before and after the collision.
Is linear momentum conserved?

Calculate the kinetic energy of each cart before and after the collision.

Calculate the total kinetic energy of the system before and after the collision.
Is kinetic energy conserved?

In some cases, you may find that the measured kinetic energy before the collision
is significantly different from the measured kinetic energy after the collision:
is kinetic energy not conserved in these collisions? In order to address this
question we have to look possible sources of energy loss such as friction. Today
we will start by reexamining our "elastic" collisions and try to reduce
the energy lost in the collisions. Some suggestions:

Reduce the separation between the two photo gates to ensure that the collision
occurs while the instantaneous velocity is being measured.

Use one or more motion sensor to measure the velocity of the one or more
of the carts (note: make sure you consider the range over which the sensors
work).

During our class today we will attempt to improve our experiments by minimizing
the losses of kinetic energy before and after our collisions. We need to realize
that our conservation laws only apply when we consider the velocities right
before and right after the collision. You can use the setup used in experiment
P17 as a starting point and use the setup window to change the setup of
the sensors being used. A scientist tries to improve his or her experiments
on a daily basis. Today is your turn!

In inelastic collisions, kinetic energy is not conserved, and some of the
kinetic energy is converted into internal energy (e.g. energy of deformation,
heat,
etc.). Using the same setup we used in experiment
P17 we will study today inelastic collisions (in which the carts stick
together after the collision). In order to carry out inelastic collisions,
we use the
velcro bumpers on the carts so that the carts stick together after the collision.
Following the same procedure we used in our studies of elastic collisions,
carry
out a series of measurements with different initial velocities. For each collision
carry out the following calculations:

Calculate the linear momentum of each cart before and after the collision.

Calculate the total linear momentum of the system before and after the collision.
Is linear momentum conserved?

Calculate the kinetic energy of each cart before and after the collision.

Calculate the total kinetic energy of the system before and after the collision.
How much energy is lost in the collision?

Repeat the series of inelastic collisions after changing the mass of the carts
(study at least two additional combinations of cart masses).

The lab report that is due next week should focus on conservation laws. We
have looked at conservation of energy and linear momentum for
both elastic and inelastic collisions in one dimension, using experiment 17.
Your lab report should describe these measurements and study the conservation
of energy and linear momentum
in one dimension by discussing the results of the data obtained in
experiment 17.